Disclaimer: the following information is based on my own personal speculation, understanding, and insight. Take it at face value.
But I do not think there is a "too much" amount of snow on ice. A lot of factors go into the safety. I had many questions about snow on the ice but after getting responses from people combined with the research I could find on the matter, it is not black and white. A lot of snow does slow down the formation of ice due to insulation. But if there is already a solid amount of ice, snow works to insulate in the opposite direction in terms of the ice melting. Kind of like a cooler or thermos, keeps cold things cold and hot things hot. The snow acts as a buffer from the air temperature to the ice. In terms of weight, it does not seem to have a big impact on the structural safety or breaking point of the ice. The weight of the snow is evenly distributed (assuming the ice is not on a pressure ridge or sagging from a sudden decrease in water levels). With the weight being evenly distributed, it pushes the ice down into the water but does not add to risk of breaking. It will push the ice down which causes water to flow up onto the ice though. This leads to the nasty slush everyone groans about. On some of the water I ice fish, there is typically 10"-20" of white ice on top of the clear, black ice. There is usually some notable amount of water in the bottom layers of the white ice. All of the white ice is snow that has mixed with water and refreezes. I have definitely noticed that there is significantly less clear, black ice underneath areas that have a lot of white ice. So I can attest to the fact that the snow acts as an insulating barrier which prevents the formation of good solid ice.
I hope this long winded post holds some insights for you (and also hope that nothing is far from truth
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